AMP MATH VIDEO LIBRARY

 

 

 

1. Fermat's Last Theorem-The Theorem and its Proof: An Exploration of Issues and Ideas.

 

"`Fermat Fest: The Video' successfully brings to life one of the most dramatic episodes in the history of mathematics. A superb cast of speakers and a lively soundtrack featuring such hits as Tom Lehrer's `There's a delta for every epsilon' and `That's mathematics' (with original lyrics to celebrate Wiles' achievement) make this an ideal entertainment and educational value for the undergraduate classroom, mathematical parties, and indeed for the whole family ... All in all, `Fermat Fest: The Video' definitely rates an enthusiastic 'thumbs-up', and is sure to delight mathematicians and non-scientists alike."

 

-- Mathematical Reviews

 

Description

In July 1993, just three weeks after Andrew Wiles's announcement of a proof of Fermat's Last Theorem, the Mathematical Sciences Research Institute hosted a special celebration in San Francisco. Combining mathematics, history, and music, the evening of public lectures was a great success. This videotape captures the celebratory mood of what has come to be known as the "Fermat Fest", with talks by five mathematicians, musical interludes, and a panel discussion. Accessible to a general audience and requiring no mathematical background, the videotape provides insight into the mathematics and the history of this famous problem. Accompanying the tape is a pamphlet in which some of the speakers present additional background material; also included are an article by Hendrik Lenstra on Pythagorean triples and one by Joe Buhler on the contributions of Sophie Germain. This tape is an excellent means for stimulating student interest in mathematics, as it presents some fascinating mathematical concepts while also revealing the human side of attempts to solve this famous problem. The tape is closed-captioned.

 

Moderator: Will Hearst; Speakers: Robert Osserman, Lenore Blum, Karl Rubin, Kenneth Ribet, John H. Conway; Panelists: Lenore Blum, John H. Conway, Lee Dembart, Kenneth Ribet; Musician: Morris Bobrow.

 

This tape is produced by MSRI and distributed by the American Mathematical Society.

 

            Publisher: MSRI

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1994

ISBN: 0-9639903-0-6

Duration: 90 minutes

 

2. Modular Elliptic Curves and Fermat's Last Theorem

 

"Accessible to advanced undergraduates and graduate students with some background in algebra and number theory."

 

-- Zentralblatt MATH

 

Description

In 1637, Pierre de Fermat wrote his legendary marginal comment that xn+yn=zn has no solution in positive integers when n≥3. Fermat's Last Theorem has eluded proof over the centuries, stimulating a great deal of mathematical development. In 1993, Andrew Wiles announced his proof of this celebrated theorem. Wiles's main result, a special case of the Taniyama Conjecture, relies on a wide range of mathematical tools developed over the past ten years. A crucial link was a 1986 theorem that the Taniyama Conjecture implies Fermat's Last Theorem, proved by Kenneth Ribet, who gives the two lectures on this videotape. Presented just weeks after Wiles's now-historic announcement, these expository lectures describe the main ingredients in Wiles's results. The lectures would be accessible to advanced undergraduates and graduate students with some background in algebra and number theory.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1993

ISBN: 0-8218-8087-X

Duration: 100 minutes

 

 

3. A Conversation with Paul Halmos

 

Description

Halmos, mathematician, writer, lecturer, and teacher extraordinaire, begins by telling his audience, "I'm scared stiff!" In this candid interview, Halmos in his inimitable fashion, talks about teaching, students, the value of experiment in teaching, calculus reform, the Moore Method, changes in teachers and students over the last twenty years, and personal reminiscences of famous mathematicians he has known. A must for all Halmos' fans.

 

            Publisher: Mathematical Association of America

Duration: 40 minutes

 

4. N is a Number: A Portrait of Paul Erdos

This well-shot program is an excellent choice for mathematics students and others familiar with Erdos' accomplishments.

 

-- Booklist

 

I strongly believe that most high school students, science and mathematics teachers, and administrators will enjoy watching this films. I give it two thumbs up!

 

-- The Mathematics Teacher

           

            Description

A man with no home and no job, Paul Erdos was the most prolific mathematician who ever lived. Universally revered among mathematicians, Erdos, who was born in Hungary in 1913, was a wandering genius who eschewed the traditional trappings of success, dedicating himself instead to inventing new problems and searching for their solutions. He inspired generations of mathematicians throughout the world with his insightful approach and the wry humor with which he discusses politics, death, and the cosmic struggle to uncover proofs hidden by the most stubborn of adversaries - God.

N is a Number, a documentary filmed in England, Hungary, Poland and the United States over four years, presents Erdos's mathematical quest in its personal and philosophical dimensions, and the tragic historical events that molded his life. N is a Number was made with support from the American Mathematical Society, Film Arts Foundation, the Heineman Foundation, the Mathematical Association of America and the National Science Foundation's Informal Science Education Program.

 

Duration: 58 minutes

 

5. Let Us Teach Guessing. George Pólya

 

            Description

In a remarkable tour de force, Pólya shows us how to teach guessing. In this classic film, master teacher Pólya leads an undergraduate class to discover the number of parts into which 3-space is divided by five arbitrary planes.

 

1966, color, 61 minutes

 

6. MAA Calculus Films in Video Format

 

            Description

This series of films was produced by the MAA in the late 60s.The films range in style from informational scripted graphics with hand-painted gels to humorous cartoons. Some films present informal introductions to topics from calculus; others include precise, detailed investigations. Each tape is approximately 60 minutes in length.

 

Tape 1:

A Function is a Mapping

Continuity of Mappings

Limit

I Maximize

Theorem of the Mean Policeman

60 minutes

 

Tape 2:

Newton's Method

The Definite Integral as a Limit

Fundamental Theorem of the Calculus

What is Area?

60 minutes

 

Tape 3:

Area Under a Curve

The Definite Integral

The Volume of a Solid of Revolution

Volume by Shells

Infinite Area

60 minutes

 

7. Careers in Mathematics

 

            Description

The "Careers in Mathematics" video contains interviews with mathematicians working in industry, business and government. The purpose of the video is to allow the viewer to hear from people working outside academia what their day-to-day work life is like and how their background in mathematics contributes to their ability to do their job. Interviews were conducted on site, showing the work environment and some of the projects mathematicians contributed to as part of multidisciplinary teams. People interviewed come from industrial based firms such as Kodak and Boeing, business and financial firms such as Price Waterhouse and D. E. Shaw & Co., and government agencies such as the National Institute of Standards and Technology and the Naval Sea system Command.

 

Careers in Mathematics was developed jointly by the American Mathematical Society (AMS), the Society for Industrial and Applied Mathematics (SIAM), and the Mathematical Association of America (MAA).

 

Publisher: American Mathematical Society, Society for Industrial and Applied Mathematics, Mathematical Association of America with funding by the Sloan Foundation.

Distributor: American Mathematical Society

Publication Year: 2001

ISBN: 0-7872-6790-2

Duration: 35 minutes

 

8. Preparing for Careers in Mathematics

Organized by: Annalisa Crannell, Franklin & Marshall College, Lancaster, PA

Speakers: Steven J. Altschuler, Microsoft Corporation, Redmond, WA, William Browning, Applied Mathematics, Inc., Gales Ferry, CT, Ray E. Collings, DeKalb College, Clarkston, GA, Margaret Holen, Lehman Brothers, New York, NY, Sandra L. Rhoades, Keene State College, NH, James R. Schatz, National Security Agency, Ft. George G. Meade, MD, Anita Solow, DePauw University, Greencastle, IN, and Francis Edward Su, Harvey Mudd College, Claremont, CA.

 

Description

This video presents an edited version of a panel discussion that took place at the Joint Mathematics Meetings in Seattle in August 1996. The panel, sponsored by the AMS Committee on the Profession, discussed how Ph.D. students in mathematics can prepare themselves for finding jobs once they finish their degrees. The panelists ranged from new Ph.D.s who had recently been on the job market to senior mathematicians in academia and industry. Among the topics discussed are how to start preparing for a job search while still a graduate student, specific job search strategies, tips on interviewing, and perspectives on what academic and industrial employers are looking for in a job applicant. The video ends with a look at the range of employment resources offered by the AMS.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: AMS-MAA Joint Lecture Series

Publication Year: 1997

ISBN: 0-8218-0839-7

Duration: 30 minutes

 

9. Introduction to Geometric Probability. Gian-Carlo Rota

     

 

"This lecture examines the notion of invariant measure from a fresh viewpoint. Master expositor Gian Carlo-Rota shows how, starting with a few simple axioms, one can concoct new invariant measures and explore their properties. One set of such measures, known as the intrinsic volumes, are quite new and still somewhat mysterious. However, they have intriguing probabilistic interpretations and in fact can be shown to form a basis for the space of all continuous invariant measures. Rota also discusses the remarkable connection between the intrinsic volumes and the Euler characteristic. Reaching deep ideas while remaining at an elementary level, this lecture would be accessible to undergraduate mathematics majors."

 

-- Zentralblatt MATH

 

"Since this remarkable member of the mathematical community died on April 19, 1999, we are fortunate to have a visual record of his lecture. Arthur Jaffe's introductory remarks, not found in the printed article, give a summary of Rota's many accomplishments."

 

-- Mathematical Reviews

 

Description

This lecture examines the notion of invariant measure from a fresh viewpoint. The most familiar examples of invariant measures are area and volume, which are invariant under the group of rigid motions. Master expositor Gian-Carlo Rota shows how, starting with a few simple axioms, one can concoct new invariant measures and explore their properties. One set of such measures, known as the intrinsic volumes, are quite new and still somewhat mysterious. However, they have intriguing probabilistic interpretations and in fact can be shown to form a basis for the space of all continuous invariant measures. Rota also discusses the remarkable connection between the intrinsic volumes and the Euler characteristic. Reaching deep ideas while remaining at an elementary level, this lecture would be accessible to undergraduate mathematics majors.

 

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Publication Year: 1999

ISBN: 0-8218-1351-X

Duration: 60 minutes

 

10. Interview with I. M. Gelfand

 

Description

In this one-hour interview, I. M. Gelfand, one of the major mathematicians of the century, discusses his mathematics, his inspirations, and his major achievements. He also touches on his work in biology and education, two areas in which he has had an important impact. The interview was held during the Joint Mathematics Meetings in Baltimore in January 1992, not long after Gelfand left the former Soviet Union to take a position at Rutgers University. Providing a personal look at this great mathematician, the interview will have particular appeal for students, researchers, and historians in mathematics and science. In addition, because Gelfand avoids discussing technical aspects of his work and focuses on what interests and inspires him as a mathematician, this videotape would be accessible to a general audience.

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1993

ISBN: 0-8218-8084-5

Duration: 60 minutes

 

11. Some Mathematics of Baseball. Henry O. Pollak

     

 

"Pollack is lively, entertaining and engaging as he steps through the problems. His methods of using the statistics of a great game to demonstrate mathematics will surely delight anyone with even the remotest interest in baseball ... this was far and away the most interesting analysis of world series events that I have seen in four decades of following the sport ... an excellent way to teach algebra or probability by demonstrating a real-world problem with serious consequences."

 

-- Mathematics and Computer Education

 

Description

Get out your mitts, your baseballs, your bats--and your calculators? This videotape of the 1991 Pi Mu Epsilon J. Sutherland Frame Lecture presents a delightful tour through a myraid of ways of applying mathematics to baseball; and the best thing is, you don't have to be a baseball fan to enjoy it! Witty, engaging, and indefatigable, Pollak pursues his topic with a passion: "Once this gets in your blood, you just don't stop!" He doesn't just stick to those dry statistics that sportswriters bandy about--he actually builds models to analyze the game and discusses why the models work in some ways and don't in others. Well-paced and lucid, with a judicious use of numbers and calculations, the lecture is accessible to students having a familiarity with basic probability theory. It makes an excellent classroom enrichment tool, especially when shown around the time of the World Series.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1993

ISBN: 0-8218-8083-7

Duration: 60 minutes

 

12. Descartes and Problem Solving. Judith Grabiner

     

Description

This videotape captures a lively, vivid, and meticulously researched lecture by the noted mathematical historian Judith Grabiner. In looking at Descartes' approach to problem solving, Grabiner brings into focus his general philosophy that, unless one has method, one will never discover anything useful. His general method was to reduce a geometric problem to an algebraic one and then construct a curve that solves the algebraic problem. Grabiner demonstrates how Descartes used this method in a particular situation. Connecting this mode of thinking to the history that preceded Descartes, she shows how he combined, extended, and exploited earlier methods. The lecture is accessible to undergraduates with an interest in mathematics and would make a fine supplement to a course in mathematics or mathematics history.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1992

ISBN: 0-8218-8069-1

Duration: 60 minutes

 

13.  Pedagogical Peeves and Other Complaints of Age: Crazy Al, Still Teaching Calculus after All These Years. Al Novikoff

 

Description

At times wildly funny, always thought-provoking, this videotaped lecture provides insight into some of the central problems in teaching and learning calculus. Although such student foibles as f(x+y)=f(x)+f(y) make Novikoff want to "sue in the World Court," he also has great sympathy for the genuine confusion students feel when confronted with supposedly clear mathematical explanations that actually obscure the basic ideas of the subject. Presenting a smorgasbord of specific examples, Novikoff builds his basic point: mathematics makes sense, but textbooks and teachers often don't. His examples not only can help teachers of calculus improve their presentations of particular topics, but also reflect a teaching philosophy that emphasizes responding to students, what they know and what they don't, what makes sense to them and what doesn't. Anyone who teaches mathematics will appreciate this engaging and insightful lecture.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1992

ISBN: 0-8218-8071-3

Duration: 60 minutes

 

14. The Mysteries of Space. Michael Atiyah, Trinity College, Cambridge, England

     

 

"This video tape provides a good opportunity to enjoy the vivid lecturing style of Sir Michael Atiyah."

 

-- Zentralblatt MATH

 

Description

From the earliest times, the geometry of space has been intimately involved with physics. As science has evolved and our understanding has deepened, the relations between geometry and physics have become subtler and more complex. At the present time, fundamentally new ideas from both areas are dramatically altering conceptions about the nature of the universe. In this videotaped presentation, Sir Michael Atiyah, one of the foremost mathematicians of this century, discusses some of the recent deep connections that have been discovered between mathematics and quantum physics. Starting with the viewpoints of Euclid and Newton, Atiyah moves on to current ideas growing out of Jones' work on knots in 3-space and Donaldson's work on 4-manifolds. In describing how Witten has brought these developments into contact with quantum field theory, Atiyah shows how quantum field theory is in itself an effort to understanding the structure of a vacuum. A witty, engaging, and clear-sighted lecturer, Atiyah makes this fascinating topic accessible to audiences with a general scientific background.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1992

ISBN: 0-8218-8076-4

Duration: 60 minutes

 

15. Algebra as a Means of Understanding Mathematics. Saunders Mac Lane

 

"Accessible to those at the level of an advanced undergraduate."

 

-- Mathematical Reviews

 

Description

What is the real nature of algebra? How does algebra help us to gain insight into other areas of mathematics? Saunders MacLane probes these and other questions. In a lecture that ranges from categories to braids, from tensor products to spectral sequences, MacLane shows how algebra forms a common thread uniting them all. The lecture is accessible to advanced undergraduates. (Columbus, OH, 1990)

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: AMS-MAA Joint Lecture Series

Publication Year: 1991

ISBN: 0-8218-8057-8

Duration: 60 minutes

 

16. Case Studies of Political Opinions Passed Off as Science and Mathematics. Serge Lang

     

 

"An excellent choice for a colloquium or seminar meeting, this videotape exposes some of the bad things that can happen in the academic world ... good viewing for undergraduates considering a scholarly career."

 

-- Mathematics and Computer Education

 

Description

In this fascinating videotaped presentation, Serge Lang discusses his nationally publicized battle against what he sees as quantitative verbiage used by some people in the social sciences to pass off political opinions as science. The central part of the lecture focuses on some works of Samuel Huntington, a well-known political scientist who was rejected by the National Academy of Sciences, partly as a result of Lang's campaign against him. Quoting from original sources, Lang documents how Huntington and other authors not only misused what some people call mathematics by assigning numerical values to various social phenomena (such as a "frustration index" for a society), but also misrepresent historical facts. Lang describes reactions in the social science community, in the press, and those of several students who used Huntington's textbooks in their classes.

 

Never one to shy away from controversy over causes he believes in, Lang devoted a great deal of time and energy into what he sees as a crucial fight for standards and integrity in academia. His story raises challenging questions about the standards that scholars set for themselves, their institutions, and their colleagues. The lecture would be suitable for students and scholars in any academic discipline. A writeup of the talk, with references, is included. (Boulder, CO, 1989)

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: AMS-MAA Joint Lecture Series

Publication Year: 1991

ISBN: 0-8218-8037-3

Duration: 60 minutes

 

17. Von Neumann Algebras in Mathematics and Physics. Vaughan F. R. Jones

     

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: ICM Series

Publication Year: 1991

ISBN: 0-8218-8053-5

Duration: 60 minutes

18.  ax2 + hxy + cy2 = n. John H. Conway

     

Description

The quadratic forms of the type in the title of this lecture lead to a beautiful picture in the hyperbolic plane--a picture that not only allows for understanding of the deeper properties of these forms but also leads to an algorithm for their solution. Taking viewers on a trip down "the river," with a forest of positive integers on one side, and negative integers on the other, Conway shows how this simple representation elucidates certain properties of the forms. The videotape is appropriate for advanced undergraduates with background in number theory. (Boulder, CO, 1989)

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: AMS-MAA Joint Lecture Series

Publication Year: 1990

ISBN: 0-8218-8027-6

Duration: 60 minutes

 

19. Matrices I Have Met. Paul Halmos

 

 

Description

Imbued with Halmos's inimitable charm and wit, this is not so much a lecture as a friendly chat, and will spark the interest of anyone with even a minimal understanding of matrix algebra. (New Orleans, LA, 1986)

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: AMS-MAA Joint Lecture Series

Publication Year: 1986

ISBN: 0-8218-8017-9

Duration: 60 minutes

 

20. In Search of Symmetry. William Browder

     

"The reviewer recommends enthusiastically this tape to the mathematical community, in particular those interested in algebraic topology and its applications to transformation groups."

 

-- Zentralblatt MATH

 

Description

William Browder served as President of the American Mathematical Society during 1990-1991. This videotape contains his Retiring Presidential Address--which combined short remarks about his presidency with a mathematical lecture--preceded by an informal interview in which he discusses a range of topics, including public awareness of mathematics and his interest in music. The lecture discusses the action of finite groups on manifolds, exploring the question of how large a finite group can effectively act on a given manifold (here, "effectively" means that there is no subgroup that fixes everything). A related question is, what kind of spaces have the given manifold as a covering space? Beginning with the historical roots of these questions, Browder concentrates on familiar examples such as the sphere, the n-sphere, or a product of spheres of different dimensions. The lecture is accessible to mathematics majors with background in algebraic topology. The interview segment provides a fine complement to the lecture.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1994

ISBN: 0-8218-8091-8

Duration: 90 minutes

 

21. The Moore Method. A Documentary on R. L. Moore

 

Description

In this film shot in his classroom, Moore passionately explains his methods of teaching which placed preeminent value on students discovering mathematics on their own. Moore also reflects on the beginnings of his own mathematical education in 1877.

 

1966, color, 55 minutes

 

22. The Story of Pi

 

            Description

Although  π is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles. Animated sequences dissect a circular disk of radius r and transform it to a rectangle of base π r and altitude r. Animation shows how Archimedes estimated π using perimeters of approximating polygons.

 

Duration: 24 minutes

 

23. John von Neumann. A Biography

 

            Description

Rare footage and photographs of the legendary von Neumann are to be found in this film biography. Halmos, Morgenstern, Teller, Wigner, and Ulam contribute insights about and memories of Johnny.

1966, b&w, 63 minutes

 

24. A New Look at Knot Polynomials. Joan Birman

 

"An excellent introduction to the theory of knots."

 

-- Zentralblatt MATH

 

Description

This videotape combines a lecture with an informal interview to bring out the fascination of the subject of knot polynomials as well as a personal view of the field from one of its leaders. In the interview portion of the tape, Birman discusses her role in the discovery of the celebrated Jones polynomial, how she got started in knot theory, and some of the changes she has seen in the field. Birman's lecture, widely praised at the 1992 Joint Mathematics Meetings in Baltimore as one of the best introductions to the subject, balances the intuition of pictures with the rigor of technical details. Because she starts with the basic definition of a knot and moves up to the latest developments involving Vassiliev invariants, this lecture will interest undergraduates and researchers alike.

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: AMS-MAA Joint Lecture Series

Publication Year: 1993

ISBN: 0-8218-8078-0

Duration: 60 minutes

 

25. The Teaching of Calculus: Careful Changes. Gilbert Strang

     

Description

Well known for his textbooks and his attention to students, Gilbert Strang has some novel ideas about how to teach calculus. In this insightful videotaped lecture, Strang discusses how concepts that commonly confuse students can be used as springboards to better understanding. For example, students often confuse the functions x3 and 3x. In fact, for some values of x, the graphs of these two functions look very similar and actually cross in two places. Using a computer to plot such functions avoids "flooding the course with numbers", as Strang puts it, and improves the students' ability to visualize. He shows how looking at integration numerically on a computer can help students to better understand infinitesimals. He also presents computer "experiments" with iterations of functions that produce surprising and intriguing results. This videotape is useful to anyone interested in new ways to teach calculus and mathematics in general.

 

 

Publisher: American Mathematical Society

Distributor: American Mathematical Society

Series: Selected Lectures

Publication Year: 1992

ISBN: 0-8218-8068-3

Duration: 60 minutes

 

26. George Lusztig, Intersection cohomology methods in representation theory

 

Talk at the International Congress of Mathematicians 1990

 

 

 

 

Acknowledgment of support:

Supported by the National Science Foundation under Grant No. HRD-0331537.